A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam.

Casimir effect on the pull-in parameters of nanometer switches. Microsys Technol

This paper investigates the thermo-electro-mechanical vibration of the rectangular piezoelectric nanoplate under various boundary conditions based on the nonlocal theory and the Mindlin plate theory. It is assumed that the piezoelectric nanoplate is subjected to a biaxial force, an external electric voltage and a uniform temperature rise. The Hamilton's principle is employed to derive the governing equations and boundary conditions, which are then discretized by using the differential quadrature (DQ) method to determine the natural frequencies and mode shapes. The detailed parametric study is conducted to examine the effect of the nonlocal parameter, thermo-electro-mechanical loadings, boundary conditions, aspect ratio and side-to-thickness ratio on the vibration behaviors.

Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions

DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix

In this study, an analytical method of the small scale parameter on the vibration of single-walled Boron Nitride nanotube (SWBNNT) under a moving nanoparticle is presented. SWBNNT is embedded in bundle of carbon nanotubes (CNTs) which is simulated as Pasternak foundation. Using Euler–Bernoulli beam (EBB) model, Hamilton's principle and nonlocal piezoelasticity theory, the higher order governing equation is derived. The effects of electric field, elastic medium, slenderness ratio and small scale parameter are investigated on the vibration behavior of SWBNNT under a moving nanoparticle. Results indicate the importance of using surrounding elastic medium in decrease of normalized dynamic deflection. Indeed, the normalized dynamic deflection decreases with the increase of the elastic medium stiffness values. The electric field has significant role on the nondimensional fundamental frequencies, as a smart controller. The results of this work is hoped to be of use in design and manufacturing of smart nano-electro-mechanical devices in advanced medical applications such as drug delivery systems with great applications in biomechanics.

Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle

Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle

Recently, the mechanical behavior of micro-/nano-structures has sparked an ongoing debate, which leads to a fundamental question: what steps can be taken to investigate the mechanical characteristics of these structures, and characterize their performance? From the standpoint of the non-classical behavior of materials, size-dependent theories of micro-/nano-structures can be considered to analyze their mechanical behavior. The application of classical theories in the investigation of small-scale structures can lead to inaccurate results. Many studies have been published in the past few years, in which continuum mechanics models have been used to investigate micro-/nano-structures with different geometry such as rods, tubes, beams, plates, and shells. The mechanical behavior of these systems under different loading – resulting in vibration, wave propagation, bending, and buckling phenomena – is the focus of the review covered in this work. The present objective is to provide a detailed survey of the most significant literature on continuum mechanics models of micro-/nano-structures, and thus orient researchers in their future studies in this field of research.

A review of size-dependent continuum mechanics models for micro- and nano-structures

Longitudinal magnetic field effect on wave propagation of fluid-conveyed SWCNT using Knudsen number and surface considerations

Frequency analysis and forced vibration response of fluid conveying viscoelastic nanotubes that resting on nonlinear visco-pasternak foundation under magnetic field using size-dependent non-local strain gradient theory are considered in this study. It is supposed that the nanotube is modelled as cantilever type beam and subjected to a harmonic load. The material property of the nanotube is modelled by Kelvin-Voigt viscoelastic constitutive relation and slip boundary conditions of nanotube conveying fluid are taken into account. Extended Galerkin method is used to obtain the nonlinear differential equation of the motion and the multiple time-scales method is utilised to investigate the primary vibration resonance of the nanotube. Firstly, the frequency analysis is performed on the linear system and the effects of foundation coefficients on the natural frequency are investigated at several flow velocities. Moreover, the resonance properties of the system are solved in closed form and analysed from the frequency-response curves, and then the effects of the non-local parameter, length scale parameter and magnetic field are fully investigated. In this case, non-local parameter, length scale parameter and foundation coefficients are highly influential on the frequency response of the considered system.

Mir Abbas Roudbari

Papers

Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle

Nonlocal piezoelastic surface effect on the vibration of visco-Pasternak coupled boron nitride nanotube system under a moving nanoparticle

A review of size-dependent continuum mechanics models for micro- and nano-structures

Longitudinal magnetic field effect on wave propagation of fluid-conveyed SWCNT using Knudsen number and surface considerations

Nonlinear vibration of fluid conveying cantilever nanotube resting on visco-pasternak foundation using non-local strain gradient theory